Assignment 1
Adrianne Kristianto
1/26/2021
Question 8
This exercise relates to the College data set, which can be found in the file College.csv. It contains a number of variables for 777 different universities and colleges in the US.
8A: Use the read.csv() function to read the data into R. Call the loaded data college. Make sure that you have the directory set to the correct location for the data.
library(ISLR)
data(College)
college <- read.csv("College.csv")8B: Look at the data using the fix() function. You should notice that the first column is just the name of each university. We don’t really want R to treat this as data. However, it may be handy to have these names for later.
head(college[, 1:5])## X Private Apps Accept Enroll
## 1 Abilene Christian University Yes 1660 1232 721
## 2 Adelphi University Yes 2186 1924 512
## 3 Adrian College Yes 1428 1097 336
## 4 Agnes Scott College Yes 417 349 137
## 5 Alaska Pacific University Yes 193 146 55
## 6 Albertson College Yes 587 479 158However, we still need to eliminate the first column in the data where the names are stored.
college <- college [,-1]
head(college[, 1:5])## Private Apps Accept Enroll Top10perc
## 1 Yes 1660 1232 721 23
## 2 Yes 2186 1924 512 16
## 3 Yes 1428 1097 336 22
## 4 Yes 417 349 137 60
## 5 Yes 193 146 55 16
## 6 Yes 587 479 158 38Now you should see that the first data column is Private. Note that another column labeled row.names now appears before the Private column. However, this is not a data column but rather the name that R is giving to each row.
8C(i): Use the summary() function to produce a numerical summary of the variables in the data set.
summary(college)## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate
## Min. : 10.00
## 1st Qu.: 53.00
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.008C(ii): Use the pairs() function to produce a scatterplot matrix of the first ten columns or variables of the data. Recall that you can reference the first ten columns of a matrix A using A[,1:10].
pairs(college[,1:10])
8C(iii): Use the plot() function to produce side-by-side boxplots of Outstate versus Private.
plot(college$Private, college$Outstate, xlab = "Private University", ylab ="Out of State tuition (USD)", main = "Out of State Tuition Plot", col = c('powderblue', 'mistyrose'))
8C(iv): Create a new qualitative variable, called Elite, by binning the Top10perc variable. We are going to divide universities into two groups based on whether or not the proportion of students coming from the top 10 % of their high school classes exceeds 50 %.
Elite=rep("No",nrow(college ))
Elite[college$Top10perc >50]=" Yes"
Elite=as.factor(Elite)
college=data.frame(college , Elite)Use the summary() function to see how many elite universities there are. Now use the plot() function to produce side-by-side boxplots of Outstate versus Elite.
summary(college$Elite)## Yes No
## 78 699plot(college$Elite, college$Outstate, xlab = "Elite University", ylab ="Out of State tuition (USD)", main = "Out of State Tuition Plot", col = c('#b492ff', '#baffc5'))
8C(v): Use the hist() function to produce some histograms with differing numbers of bins for a few of the quantitative variables. You may find the command par(mfrow=c(2,2)) useful: it will divide the print window into four regions so that four plots can be made simultaneously. Modifying the arguments to this function will divide the screen in other ways.
par(mfrow=c(2,2))
hist(college$F.Undergrad, xlab = "Full-time Undergraduates", ylab = "Count", main = "Histogram of Full-time Undergraduates", col= "#c16e6e")
hist(college$Personal, xlab = "Personal Spending", ylab = "Count", main = "Histogram of Estimated Personal Spending", col = "#d39797")
hist(college$Grad.Rate, xlab = "Rate", ylab = "Count", main = "Histogram of Graduation Rate", col = "#9a5656")
hist(college$Room.Board, xlab = "Cost", ylab = "Count", main = "Histogram of Room and Board Costs", col = "#7d2d2d")
8C(vi): Continue exploring the data, and provide a brief summary of what you discover.
summary(college$Outstate)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2340 7320 9990 10441 12925 21700Summary: The code chunk above shows that the highest out-of-state tuition for universities in the US is $21,700. Let’s see which university has the highest out-of-state tuition.
outstate <- college[college$Outstate == 21700, ]
rownames(outstate)## [1] "48"Looking back at the dataset, we can see that Bennington College (48) has the highest out-of-state tuition fee
Question 9
This exercise involves the Auto data set studied in the lab. Make sure that the missing values have been removed from the data.
str(Auto)## 'data.frame': 392 obs. of 9 variables:
## $ mpg : num 18 15 18 16 17 15 14 14 14 15 ...
## $ cylinders : num 8 8 8 8 8 8 8 8 8 8 ...
## $ displacement: num 307 350 318 304 302 429 454 440 455 390 ...
## $ horsepower : num 130 165 150 150 140 198 220 215 225 190 ...
## $ weight : num 3504 3693 3436 3433 3449 ...
## $ acceleration: num 12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
## $ year : num 70 70 70 70 70 70 70 70 70 70 ...
## $ origin : num 1 1 1 1 1 1 1 1 1 1 ...
## $ name : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...Q9A: Which of the predictors are quantitative, and which are qualitative?
- All predictors are quantitative except for
name
Q9B: What is the range of each quantitative predictor? You can answer this using the range() function.
summary(Auto[, -9])## mpg cylinders displacement horsepower weight
## Min. : 9.00 Min. :3.000 Min. : 68.0 Min. : 46.0 Min. :1613
## 1st Qu.:17.00 1st Qu.:4.000 1st Qu.:105.0 1st Qu.: 75.0 1st Qu.:2225
## Median :22.75 Median :4.000 Median :151.0 Median : 93.5 Median :2804
## Mean :23.45 Mean :5.472 Mean :194.4 Mean :104.5 Mean :2978
## 3rd Qu.:29.00 3rd Qu.:8.000 3rd Qu.:275.8 3rd Qu.:126.0 3rd Qu.:3615
## Max. :46.60 Max. :8.000 Max. :455.0 Max. :230.0 Max. :5140
## acceleration year origin
## Min. : 8.00 Min. :70.00 Min. :1.000
## 1st Qu.:13.78 1st Qu.:73.00 1st Qu.:1.000
## Median :15.50 Median :76.00 Median :1.000
## Mean :15.54 Mean :75.98 Mean :1.577
## 3rd Qu.:17.02 3rd Qu.:79.00 3rd Qu.:2.000
## Max. :24.80 Max. :82.00 Max. :3.000Q9C: What is the mean and standard deviation of each quantitative predictor?
sapply(Auto[, -9], mean)## mpg cylinders displacement horsepower weight acceleration
## 23.445918 5.471939 194.411990 104.469388 2977.584184 15.541327
## year origin
## 75.979592 1.576531sapply(Auto[, -9], sd)## mpg cylinders displacement horsepower weight acceleration
## 7.8050075 1.7057832 104.6440039 38.4911599 849.4025600 2.7588641
## year origin
## 3.6837365 0.8055182Q9D: Now remove the 10th through 85th observations. What is the range, mean, and standard deviation of each predictor in the subset of the data that remains?
subset <- subset(Auto[-(10:85), -9])
sapply(subset, range)## mpg cylinders displacement horsepower weight acceleration year origin
## [1,] 11.0 3 68 46 1649 8.5 70 1
## [2,] 46.6 8 455 230 4997 24.8 82 3sapply(subset, mean)## mpg cylinders displacement horsepower weight acceleration
## 24.404430 5.373418 187.240506 100.721519 2935.971519 15.726899
## year origin
## 77.145570 1.601266sapply(subset, sd)## mpg cylinders displacement horsepower weight acceleration
## 7.867283 1.654179 99.678367 35.708853 811.300208 2.693721
## year origin
## 3.106217 0.819910Q9E: Using the full data set, investigate the predictors graphically, using scatterplots or other tools of your choice. Create some plots highlighting the relationships among the predictors. Comment on your findings.
pairs(Auto[1:8]) 
Comments: From the scatter plot above, we can see that horsepower, weight, and displacement have an inverse relationship with mpg. However, horsepower, weight, and displacement have a linear/direct relationship with each other. This makes sense because horsepower is heavy. That means the more power your car has, the heavier it will become. And generally speaking, the higher an engine’s displacement the more power it can create.
Q9F: Suppose that we wish to predict gas mileage (mpg) on the basis of the other variables. Do your plots suggest that any of the other variables might be useful in predicting mpg? Justify your answer.
- Yes. As you can see from the first scatter plot, all predictors show some correlation with
mpg. For example,yearandmpgseem to have a positive relationship (as the year increases, the mpg increases) Whilehorsepowerandmpghave a negative/inverse relationship (as horsepower increases, mpg decreases. This is because higher horsepower comes from burning more fuel, so mpg is lowered)
Question 10
This exercise involves the Boston housing data set.
Q10A: To begin, load in the Boston data set. The Boston data set is part of the MASS library in R. How many rows are in this data set? How many columns? What do the rows and columns represent?
library(MASS)
str(Boston)## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...- There are 506 rows and 14 columns in this data set. The rows represent predictor observations for a neighborhood in Boston, while the columns represent predictor variables for a neighborhood in Boston.
Q10B: Make some pairwise scatterplots of the predictors (columns) in this data set. Describe your findings.
pairs(Boston)
Comments: There’s nothing much to find in this scatter plot other than the fact that some variables appear to be correlated. For example, zn and dis appear to have a fairly linear relationship as denoted by one of the scatter plots.
Q10C: Are any of the predictors associated with per capita crime rate? If so, explain the relationship.
plot(crim ~ age, data = Boston, log = "xy") #The older the house, the more crime 
plot(crim ~ tax, data = Boston, log = "xy") #The higher the tax, the more crime 
plot(crim ~ indus, data = Boston, log = "xy") #More crime in industrial areas
plot(crim ~ dis, data = Boston, log = "xy") #The closer to work area, the more crime 
plot(crim ~ rad, data = Boston, log = "xy") #Higher index of accessibility to radial highway, the more crime 
Q10D: Do any of the suburbs of Boston appear to have particularly high crime rates? Tax rates? Pupil-teacher ratios? Comment on the range of each predictor.
par(mfrow=c(1,3))
hist(Boston$crim[Boston$crim > 1], breaks=25)
hist(Boston$tax, xlab = "Tax Rate", ylab = "Number of Suburbs", main = "Tax Rates", breaks=25)
hist(Boston$ptratio, xlab = "Pupil-Teacher Ratio", ylab = "Number of Suburbs", main = "Pupil-Teacher Ratio", breaks=25)
Comments: As you can see, most suburbs have low crime rates, but there are some suburbs where the crime rate is high. There’s a huge gap between suburbs with low tax rates and a peak at 660-680.
Q10E: How many of the suburbs in this data set bound the Charles river?
sum(Boston$chas == 1)## [1] 35- There are 35 suburbs bound to the Charles river
Q10F: What is the median pupil-teacher ratio among the towns in this data set?
median(Boston$ptratio)## [1] 19.05- The median would be 19 pupils for each teacher
Q10G: Which suburb of Boston has lowest median value of owneroccupied homes?
which.min(Boston$medv)## [1] 399t(subset(Boston, medv == min(medv)))## 399 406
## crim 38.3518 67.9208
## zn 0.0000 0.0000
## indus 18.1000 18.1000
## chas 0.0000 0.0000
## nox 0.6930 0.6930
## rm 5.4530 5.6830
## age 100.0000 100.0000
## dis 1.4896 1.4254
## rad 24.0000 24.0000
## tax 666.0000 666.0000
## ptratio 20.2000 20.2000
## black 396.9000 384.9700
## lstat 30.5900 22.9800
## medv 5.0000 5.0000What are the values of the other predictors for that suburb, and how do those values compare to the overall ranges for those predictors? Comment on your findings.
summary(Boston)## crim zn indus chas
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08204 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## nox rm age dis
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## rad tax ptratio black
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## lstat medv
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00Comments:
- The crime rate for Suburb 399 is relatively high compared to the average crime rate of suburbs in Boston
- There’s 0 residential land zoned for lots over 25,000sqft
- The proportion of non-retail business acres per town is slightly higher than the avg suburbs in Boston
- This suburb is not bound to the Charles river
- The nitrogen oxides concentration (parts per 10 million) is slightly higher than the avg suburbs in Boston
- Average number of rooms per dwelling is lower than the avg suburbs in Boston
- One of the suburbs that have the highest proportion of owner-occupied units built prior to 1940
- It has a low weighted mean of distances to five Boston employment centres
- Higher accessibility to radial highways
- Higher full-value property tax rate per $10,000
- Higher rate of pupil-teacher ratio by town
- Highest value for 000(Bk - 0.63)^2 where Bk is the proportion of blacks by town
- Higher status of lower population (%)
- Low median value of owner-occupied homes in $1,000
Q10H: In this data set, how many of the suburbs average more than seven rooms per dwelling? More than eight rooms per dwelling? Comment on the suburbs that average more than eight rooms per dwelling.
sum(Boston$rm > 7)## [1] 64sum(Boston$rm > 8)## [1] 13summary(subset(Boston, rm > 8))## crim zn indus chas
## Min. :0.02009 Min. : 0.00 Min. : 2.680 Min. :0.0000
## 1st Qu.:0.33147 1st Qu.: 0.00 1st Qu.: 3.970 1st Qu.:0.0000
## Median :0.52014 Median : 0.00 Median : 6.200 Median :0.0000
## Mean :0.71879 Mean :13.62 Mean : 7.078 Mean :0.1538
## 3rd Qu.:0.57834 3rd Qu.:20.00 3rd Qu.: 6.200 3rd Qu.:0.0000
## Max. :3.47428 Max. :95.00 Max. :19.580 Max. :1.0000
## nox rm age dis
## Min. :0.4161 Min. :8.034 Min. : 8.40 Min. :1.801
## 1st Qu.:0.5040 1st Qu.:8.247 1st Qu.:70.40 1st Qu.:2.288
## Median :0.5070 Median :8.297 Median :78.30 Median :2.894
## Mean :0.5392 Mean :8.349 Mean :71.54 Mean :3.430
## 3rd Qu.:0.6050 3rd Qu.:8.398 3rd Qu.:86.50 3rd Qu.:3.652
## Max. :0.7180 Max. :8.780 Max. :93.90 Max. :8.907
## rad tax ptratio black
## Min. : 2.000 Min. :224.0 Min. :13.00 Min. :354.6
## 1st Qu.: 5.000 1st Qu.:264.0 1st Qu.:14.70 1st Qu.:384.5
## Median : 7.000 Median :307.0 Median :17.40 Median :386.9
## Mean : 7.462 Mean :325.1 Mean :16.36 Mean :385.2
## 3rd Qu.: 8.000 3rd Qu.:307.0 3rd Qu.:17.40 3rd Qu.:389.7
## Max. :24.000 Max. :666.0 Max. :20.20 Max. :396.9
## lstat medv
## Min. :2.47 Min. :21.9
## 1st Qu.:3.32 1st Qu.:41.7
## Median :4.14 Median :48.3
## Mean :4.31 Mean :44.2
## 3rd Qu.:5.12 3rd Qu.:50.0
## Max. :7.44 Max. :50.0Comments:
- Suburbs that average more than 8 rooms per dwelling tend to have:
- Lower crime rates than the average suburbs in Boston (
crim) - Higher median value of owner-occupied homes in $1,000 (
medv) - Lower rate of low status population (
lstat)
- Lower crime rates than the average suburbs in Boston (